Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published February 15, 1986 | Published
Journal Article Open

Radiative transfer in a sphere illuminated by a parallel beam - an integral equation approach

Abstract

The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. Our analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the inter-connection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems are provided.

Additional Information

© 1986 American Astronomical Society. Provided by the NASA Astrophysics Data System. Received 1985 February 15; accepted 1985 June 4. We thank K. S. K. Chow, L. W. Esposito, A. J. Friedson, R. M. Goody, and N. D. Sze for helpful discussions. The search for a variational principle for the planetary problem was assigned as one of the research topics in Professor R. M. Goody's class on atmospheric radiation at Harvard in 1972. The length of time it has taken to solve the problem is perhaps a measure of the sagacity of the master and the stupidity of the pupil (Y. L. Y.). The research is supported by NASA grant NSG 7376 under the Planetary Atmospheres Program.

Attached Files

Published - 1986ApJ___301__554S.pdf

Files

1986ApJ___301__554S.pdf
Files (1.4 MB)
Name Size Download all
md5:63f7dc9cf90f020e99abaf65a1f13651
1.4 MB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 17, 2023